Algebra 1
The main goal of Algebra is to develop fluency in working with linear equations.
Students will extend their experiences with tables, graphs, and equations and solve
linear equations and inequalities and systems of linear equations and inequalities.
Students will extend their knowledge of the number system to include irrational numbers.
Students will generate equivalent expressions and use formulas. Students will simplify
polynomials and begin to study quadratic relationships. Students will use technology and
models to investigate and explore mathematical ideas and relationships and develop
multiple strategies for analyzing complex situations. Students will analyze situations
verbally, numerically, graphically, and symbolically. Students will apply mathematical
skills and make meaningful connections to life’s experiences.
Curriculum Focal Points
• Algebra: Analyzing and representing linear functions and solving linear
equations and systems of linear equations.
• Geometry and Measurement: Analyzing two- and three-dimensional space
and figures by using distance and angle.
• Data Analysis and Number and Operations and Algebra: Analyzing and
summarizing data sets.
Standard 1: Students will expand number sense to understand, perform
operations, and solve problems with real numbers.
Objective 1: Represent real numbers as points on the number line and distinguish
rational numbers from irrational numbers.
a. Define a rational number as a point on the number line that can be expressed
as the ratio of two integers, and points that cannot be so expressed as irrational.
b. Classify numbers as rational or irrational, knowing that rational numbers can
be expressed as terminating or repeating decimals and irrational numbers can be
expressed as non-terminating, non-repeating decimals.
c. Classify pi and square roots of non-perfect square numbers as irrational.
d. Place rational and irrational numbers on a number line between two integers.
Objective 2: Compute fluently and make reasonable estimates with rational and
irrational numbers.
a. Simplify, add, subtract, multiply, and divide expressions with square roots.
b. Evaluate and simplify numerical expressions containing rational numbers and
square roots using the order of operations.
c. Compute solutions to problems, represent answers in exact form, and
determine the reasonableness of answers.
d. Calculate the measures of the sides of a right triangle using the Pythagorean
Theorem.
Mathematical Language and Symbols Students Should Use
square root, √, radical, rational, irrational, Pythagorean Theorem
Standard 2: Students will extend concepts of proportion to represent and analyze
linear relations.
Objective 1: Represent and analyze the slope of a line.
a. Identify the slope of a line when given points, a graph, or an equation.
b. Identify horizontal and vertical lines given the equations or slopes.
c. Determine the effect of changes in slope or y-intercept in y = mx + b.
d. Determine and explain the meaning of slopes and intercepts using real-world
examples.
Objective 2: Model and interpret problems having a constant rate of change using
linear functions.
a. Write algebraic expressions or equations to generalize visual patterns,
numerical patterns, relations, data sets, or scatter plots.
b. Represent linear equations in slope-intercept form, y = mx + b, and standard
form, Ax+ By =C.
c. Distinguish between linear and non-linear functions by examining a table,
equation, or graph.
d. Interpret the slope of a linear function as a rate of change in real-world
situations.
Objective 3: Represent and analyze linear relationships using algebraic equations,
expressions, and graphs.
a. Write the equation of a line when given two points or the slope and a point on
the line.
b. Approximate the equation of a line given the graph of a line.
c. Identify the x- and y-intercepts from an equation or graph of a line or a table of
values.
d. Graph linear relations and inequalities by plotting points, by finding x and y
intercepts, or by using the slope and any point on the line.
Mathematical Language and Symbols Students Should Use
Slope, x-intercept, y-intercept, y = mx + b, Ax+ By =C, undefined slope
Standard 3: Students will develop fluency with the language and operations of
algebra to analyze and represent relationships.
Objective 1: Simplify polynomials and the quotient of monomials.
a. Simplify and evaluate monomial expressions and formulas.
b. Add and subtract polynomials.
c. Multiply monomials by a polynomial.
d. Multiply binomials.
e. Simplify the quotient of monomials using positive exponents.
Objective 2: Solve and interpret linear equations and inequalities in various
situations including real-world problems.
a. Solve single-variable linear equations and inequalities algebraically and
graphically.
b. Solve real-world problems involving constant rates of change.
c. Solve equations for a specified variable.
d. Solve proportions that include algebraic first-degree expressions.
Objective 3: Solve and interpret pairs of linear equations and inequalities.
a. Solve systems of two linear equations graphically and algebraically with and
without technology.
b. Determine the number of possible solutions for a system of two linear
equations.
c. Graph a system of linear inequalities and identify the solution.
Objective 4: Factor polynomials with common monomial factors and factor simple
quadratic expressions.
a. Find the greatest common monomial factor of a polynomial.
b. Factor trinomials with integer coefficients of the form x2 + bx + c.
c. Factor the difference of two squares and perfect square trinomials.
Objective 5: Solve quadratic equations using factoring or by taking square roots.
a. Solve quadratic equations that can be simplified to the form x2 = a where a ≥ 0
by taking square roots.
b. Solve quadratic equations using factoring.
c. Write a quadratic equation when given the solutions.
Mathematical Language and Symbols Students Should Use
monomial, binomial, trinomial, polynomial, literal equation, factor, difference of two
squares, perfect square, quadratic
Standard 4: Students will understand concepts from statistics and apply
statistical methods to solve problems.
Objective 1: Summarize, display, and analyze bivariate data.
a. Collect, record, organize, and display a set of data with at least two variables.
b. Determine whether the relationship between two variables is approximately
linear or non-linear by examination of a scatter plot.
c. Characterize the relationship between two linear related variables as having
positive, negative, or approximately zero correlation.
Objective 2: Estimate, interpret, and use lines fit to bivariate data.
a. Estimate the equation of a line of best fit to make and test conjectures.
b. Interpret the slope and y-intercept of a line through data.
c. Predict y-values for given x-values when appropriate using a line fitted to
bivariate numerical data.
Mathematical Language and Symbols Students Should Use
Scatter plot, positive correlation, negative correlation, no correlation, line of best fit,
bivariate